The veteran righthander pitched well in his first four starts but lost twice. A rain delay cost him one time, a lack of run support on two other occasions.

But Dempster broke through against the Houston Astros, pitching six strong innings in a 7-3 victory before a crowd of 29,312 at Fenway Park.

Dempster turns 36 next week and has been pitching in the majors for 16 seasons. A few fruitless outings were hardly a concern for him. But picking up his first victory with the Sox brought some satisfaction.

“You want to win games. I think probably more frustrating were the games that we didn’t win that I started,” Dempster said. “Wins come. Sometimes they come in bunches; sometimes they’re tough to come by.

“You keep working hard and making pitches and you put yourself in a position. You’ll win games more often than not.”

Dempster allowed two runs on four hits and struck out 10 with three walks. That dropped his earned run average to 3.30. He has struck out 43 over 30 innings.

Dempster averaged 7.2 strikeouts per nine innings when he was with the Chicago Cubs last season. That figure rose to 9.1 when he was traded to the Texas Rangers in July, and is at 12.9 this season.

How is an older pitcher who spent the bulk of his career in the National League striking out more batters in the AL?

“I don’t know, I think maybe fastball command,” Dempster said. “When you can put your fastball where you want, you end up getting ahead in the count and expand off that. Strikeouts are overrated. I’m just trying to get outs.”

Dempster said his 12 starts for Texas last season taught him to focus on an entire lineup.

“There’s not that lull at the bottom of the lineup where maybe you can pitch around a No. 8 hitter to get to the No. 9 hitter, who’s a pitcher,” he said. “You have to continue to make pitch after pitch.”

Red Sox manager John Farrell has his own theory. He thinks the key is how Dempster has used his secondary pitches, mainly his slider and split-finger fastball.

“He’s able to go to any one of three pitches in a 3-2 count or in a two-strike situation,” Farrell said. “Hitters can’t sit on any one approach to finish a guy off. He’s done such a great job at that 3-2 count where he doesn’t give in. He uses the entire count when needed. We’ve seen some of his better sliders in 3-and-2 situations.”

Catcher David Ross compared the split-finger Dempster had against the Astros to that pitch Bugs Bunny threw in the old cartoons that stopped before it got to the plate.

“It was like some Nintendo stuff,” said Ross, who had a career-high four hits, two of them home runs.

Red Sox starters are 13-4 with a 3.09 ERA. That’s why the team is tied with Texas for the best record in baseball at 16-7.

“I think it’s huge,” Dempster said. “I’m just trying to keep up with Clay and Jon and everybody. Hopefully I can go out there and continue to do my job.”

The Red Sox backed Dempster with 17 hits, nine for extra bases. Ross hit his home runs over everything in left field. David Ortiz connected for the second straight night and Will Middlebrooks hit his team-leading sixth.

“When we got some fastballs on the plate we did a very good job of driving the baseball,” Farrell said.

Houston starter Erik Bedard was back at Fenway Park for the first time since 2011, when he started eight games for the doomed Red Sox after being picked up at the trade deadline.

The laconic lefthander could not get out of the fourth inning, giving up five runs on eight hits. Bedard is 0-2 with a 7.98 ERA.

Dustin Pedroia had an RBI double in the first inning. Ross hits his first home run in the second inning, a blast that landed on the roof of the parking garage across Lansdowne Street.

The ball took a healthy bounce but did not quite make it to the Mass. Pike.

Pedroia and Napoli doubled in the third inning.

Napoli had another double in the seventh inning. It was the 18th extra-base hit for Napoli, a team record for April. His 13 doubles also are a record.

Napoli has 27 RBIs, four short of the April team record set by Manny Ramirez in 2001.

Back-to-back home runs by Middlebrooks and Ross made it 5-1 in the fourth inning.

Paul Clemens — no relation to Roger — allowed Ortiz’s home run in the fifth inning. The ball screamed into the first row of the bleachers, sending cups and caps flying.

Jonny Gomes, who had gone 46 plate appearances without an RBI, added an RBI single in the eighth inning. That raised his batting average to .189. “When the team’s winning, no one is in a slump. No one at all,” Gomes said. “I don’t consider myself in a slump. I just haven’t started yet.”

Jacoby Ellsbury was 2 for 5 with a stolen base, his 11th of the season and the 200th of his career.

Only Harry Hooper (300) and Tris Speaker (267) have more in Red Sox history. Hooper played for the team from 1909-20 and Speaker from 1907-15.

In 2009, when Ellsbury stole 70 bases, he had 10 in the first 23 games.

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